58414 - Algebra and Geometry

Course Unit Page

Academic Year 2018/2019

Learning outcomes

At the end of this course, students are supposed to have learnt some basic notions in abstract algebra (Euclidean algorithm and congruence relations) and in linear algebra. They will be able to solve linear systems and to study linear maps.

Course contents

Linear Systems


Gaussian elimination

Real vector spaces and subspaces

Linear maps

Eigenvalues and eigenvectors

 Diagonalization of matrices

Modular arithmetic, congruence classes modulo n


Fioresi Rita, Morigi Marta, Introduzione all'algebra lineare, Edizioni CEA (2015)

Teaching methods

Lectures and exercises will be alternated in order to explain theoretical concepts through a large number of examples. Students will be asked to actively participate in the lessons, asking and answering questions.

Assessment methods

The exam is both written and oral. The written exams lasts approximately two hours and consists in 4/6 exercises. Students are admitted to the oral exam after passing the written exam with at least 16/30. If a student passes the written exam, he/she mast take the oral exam either in the same "appello" or in the following one. If somebody receives less than 9/30 in the written exam, I will register officially that he did not pass the exam. If a student does not pass the oral exam, he/she must repeat the written exam.The oral exams lasts 15/20 minutes and consists in questions regarding the theory (including proofs of theorems)
The final vote is not the result of the arithmetic mean between the written and oral tests but rather the result of an overall assessment of the preparation of
the student, based on the written test which has, therefore, a decisive weight. The subjects of the examination are all and only those of the lectures
and listed in the programme available in the Professor's web page dedicated to the course.

Teaching tools

Exercises and samples of exam texts will be given.

Links to further information


Office hours

See the website of Marta Morigi